Need help with Fourier Transform fft

clc;clear all

X = [8 9 9 6 10 2 5 6];
Y = fft(X)

Hi,

Im given an index (j) (0,1,2,3,4,5,6,7), data recorded(8,9,9,6,10,3,5,6), and DFT values (7, 0.28-1.03 i,0.5,-0.78-0.03 i,1,-0.78+.03 i,0.5,0.28+1.03i). I am supposed to test my FFT algorithm to recreate the discrete Fourier transform of this data set along with recreating the discrete fourier transform by writing a program that computes the discrete fourier transform. This is what i have so far, but its giving me the wrong DFT values

Y =

Columns 1 through 6

55.0000 + 0.0000i 2.9497 - 8.9497i 4.0000 + 1.0000i -6.9497 - 0.9497i 9.0000 + 0.0000i -6.9497 + 0.9497i

Columns 7 through 8

4.0000 - 1.0000i 2.9497 + 8.9497i

Any ideas of how to start?

Thanks in advance.

[Paul]

Are you sure about the problem statement? The data and the DFT values don't seem to be consistent with each other:

fft([8 9 9 6 10 3 5 6])

ans = 
  56.0000 + 0.0000i   2.2426 - 8.2426i   4.0000 + 0.0000i  -6.2426 - 0.2426i   8.0000 + 0.0000i  -6.2426 + 0.2426i   4.0000 + 0.0000i   2.2426 + 8.2426i

[Mackenzie Weeks]

i accidentally typed 2 instead of 3, but even when thats chnaged its not outputting the DFT values that I'm supposed to be getting (7, 0.28-1.03 i,0.5,-0.78-0.03 i,1,-0.78+.03 i,0.5,0.28+1.03i)

Answer 1

[Girijashankar Sahoo]

MATLAB code DFT output is correct. You can varify it by first DFT value which is sum of data sequence

55=sum([8 9 9 6 10 2 5 6])

[Mackenzie Weeks]

oh okay i see what i did wrong! I didn't normalize my data. Once i did, I got the correct DFT values. Thanks :)